中心MHD的高阶守恒差分GLM-MHD格式
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
摘要：
我们提出并比较了三维和五阶精度有限差分格式的数值解的可压缩理想MHD方程在多个空间维度。所选择的方法依赖于四种不同的重建技术的基础上最近改进的版本的加权基本无振荡（WENO）计划，单调性保持（MP）计划，以及斜率有限的多项式重建。所提出的数值方法是高度准确的流动的光滑区域，避免损失的精度在附近的光滑极值，并提供尖锐的非振荡过渡在不连续性。我们提出了一个数值公式的基础上的细胞为中心的方法，所有的主要流量变量离散在区域中心。通过用广义拉格朗日乘子扩充MHD方程来加强无发散条件，从而产生混合双曲/抛物线校正，如Dedner等人（J. COMPUT. 175（2002）645-673）。由此产生的一系列计划是强大的，具有成本效益和简单的实施。与以前的现有方法相比，它完全避免了与椭圆发散清理步骤相关的CPU密集型工作量和交错网格算法所需的额外复杂性。广泛的数值试验表明，所提出的框架，包括光滑和不连续的功能计算的鲁棒性和可靠性。
英文摘要：
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. (J. Comput. Phys. 175 (2002) 645-673). The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.
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